Yes you almost have it spot on!
Up until the 05/04/2013 - the old rules applies, so the only consideration that is needed for the earlier years, id as a measure for the new rules.
So - she does not fall into the remit of any of the automatic oversees tests - which would allow non residency (although the second test which looks at when you have not been treated as resident in the last 3 years and will spend less than 46 days in this tax year in the UK - if the answer to this is YES (we know she was definitely not resident, but how many days so far have been spent in the UK since 06/04/2013 and how many more between now and 05/04/2014) if more than 46, then she does not meet the second automatic test and we need to move onto the automatic UK tests.
So we would then need to consider the automatic UK tests
1) She did not spend more than 183 days in the UK
2) Yes she did have a home for her use - and its a question of whether she spent more than 91 days consecutive days, of which 30 days sat in this tax year (2013/2014)
But this also considers when there is no oversees home also.
So did Mum spend more than 30 days in this UK home, but retain an oversees home? If she did then this is not an issue, if she does not have an oversees home and spent more than 30 days in the property she owns in 2013/2014 then may fall into being treated as resident for 2013/2014.
3) if you work full time in the UK for more than 365 days - which does not apply.
So then we move onto the sufficient ties test
Now Mum will fall under being treated as "not resident" for the preceding 3 years so we have to establish how many ties she had. This looks at
1) family ties - this does not apply and no husband or children under 18 in the UK
2) Accommodation ties - yes, as she will stay with you, then she either needs to spend less than 16 days each year with you (so maybe visit other family !)or accept this as one tie
3) Work tie- this does not apply
4) 90 day tie - this will apply as Mum did spend more than 90 days in either or both of the last 2 tax years
So we have two ties - this then determines that for Mum to be treated as NOT resident for this tax year (2013/2014) and assuming she has not met the Oversees automatic test and not failed on that one UK automatic test - then she is not permitted to spend more than 120 days in the UK! So you final interpretation is correct as long as she does not fail the automatic UK test as shown above.